BOSTON — But for the man who stepped in the box, such a moment couldn’t be expected in such a situation. Not when the Detroit Tigers had so handled the Boston Red Sox. Not when the totals, almost incomprehensible to that point in this American League Championship Series, showed the Red Sox with 31 strikeouts and four hits.

Yet the 38,029 who hung on Sunday night at Fenway Park — through yet another no-hit bid, this one from formidable Detroit right-hander Max Scherzer — recognized the moment for what it was, a chance, and one better than most. Down by four runs, with the bases loaded and two outs in the bottom of the eighth, it was David Ortiz in the box, and that still means something throughout New England, throughout baseball.

“I tell you what, man,” Ortiz said. “Postseason is something that it can work both ways for you. It can go well if you stay calm, or it can go bad if you try to overdo things.”

Calm? Ortiz rocked the Tigers with a game-tying missile of a grand slam in the eighth, and the night ended with a scene that seemed unfathomable for so long. The Red Sox danced across the infield chasing Jarrod Saltalamacchia, who delivered the walk-off single in a 6-5 victory that evened a series that had felt so one-sided. The next three games are in Detroit, and with Justin Verlander — a former MVP, a postseason stud — in line for the Tigers in Tuesday’s Game 3, what realistic chance did Fenway have of hosting its Red Sox again this year?

But for Ortiz, and that first-pitch swing against the change-up of Tigers closer Joaquin Benoit.

“Coming against Benoit right there, I felt something good was going to happen,” Saltalamacchia said. “I think everyone felt like something good was going to happen.”

If that was, indeed, the case, it was only because of Ortiz’s presence, his history, his flair — and all of that is significant. But even with Ortiz — who in 62 previous postseason games with Boston had 14 homers and authored some of this storied franchise’s most cherished moments — saying this was expected would be ignoring all that preceded it.

For so long, Scherzer was in line to be Sunday’s hero, and his seven-inning effort in which he allowed two hits and struck out 13 would be a gem in any ballpark in any series against any team. But consider the totality of what Detroit starters Anibal Sanchez and Scherzer did to the Red Sox over the weekend here, and what happened in the final two innings seems more unlikely. They held Boston hitters to two hits in 41 at-bats, a .049 average. They recorded a stunning 25 of their 39 outs by strikeout.

Ortiz, too, had gone hitless with four strikeouts and one walk in his first seven plate appearances of this series. So when Detroit built a 5-0 in the top of the sixth on the back of a solo homer from Miguel Cabrera and a two-run shot from Alex Avila off Boston right-hander Clay Buchholz, Fenway sagged. The Red Sox, baseball’s best offensive team during the regular season, didn’t yet have a hit, and as Scherzer carved them up, they looked very much to be pressing — Ortiz included.

“Last night, pretty much all of us were trying to overdo things,” Oritz said. “I feel like I was jumping a little bit. Even my first couple at-bats, I feel like I was doing some funny things.”

But when the eighth began, Scherzer was gone after 108 pitches, leading 5-1. “He was spent,” Detroit Manager Jim Leyland said. After an out and a double from Will Middlebrooks, out went Jose Veras for lefty Drew Smyly. A walk to Jacoby Ellsbury, and here came right-hander Al Alburquerque. A strikeout of Shane Victorino and a single from Dustin Pedroia, and here came Benoit, the closer — rather than left-hander Phil Coke, against whom the left-handed-hitting Ortiz is 2 for 18 in his career.

“Coke hadn’t pitched a big game for quite a while,” Leyland said. “Benoit is our guy against the lefties.”

Whether that remains true for the rest of the series will be determined. Ortiz, though, had studied Benoit, who Saturday night allowed the only hit the Red Sox got in Game 1.

“I know that they try to approach me better than anyone else,” Ortiz said. “They don’t want to make mistake.”

Which means he could eliminate a first-pitch fastball. He got the change-up, and he waited on it. The resulting line drive sent Tigers right fielder Torii Hunter, owner of nine Gold Gloves, charging back to the wall that separates the field from the Red Sox bullpen. He crashed into it violently, and the ball and Hunter both ended up among Boston’s relievers. Fenway, pent up for the better part of two nights, erupted. Ortiz’s October legend, secure for eternity here, was enhanced.

“On the bench, nobody’s really surprised when he does something like he does,” Saltalamacchia said. “But it’s unbelievable. You watch it on TV for so many years, and growing up watching it and then being able to be on the bench and watch that ball go out and seeing him run the bases — it’s like any other day.”

Any other day in the life of a man for whom the moment is never too big, the lights never too bright. There was still the matter of winning the game, and the Red Sox took care of that in the ninth against Rick Porcello. Jonny Gomes opened with an infield single that shortstop Jose Iglesias threw away, putting Gomes at second. Porcello then uncorked a wild pitch that allowed Saltalamacchia to change his approach, trying to drive Gomes in from third rather than just move him over from second.

And when Saltalamacchia’s grounder got through the left side of the infield, it was he who received the mob of attention, the game-winning hit. But don’t doubt that the mythical, magical aspect of Sunday night was provided David Americo Arias Ortiz, and the entire arc of the series is different because of it.

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